Azimuthal amplitude variation with offset parameterization and inversion for fracture weaknesses in tilted transversely isotropic media

The characterization of fracture-induced tilted transverse isotropy (TTI) seems to be more suitable to actual scenarios of geophysical exploration for fractured reservoirs. Fracture weaknesses enable us to describe fracture-induced anisotropy. With the incident and reflected PP-wave in TTI media, we have adopted a robust method of azimuthal amplitude variation with offset (AVO) parameterization and inversion for fracture weaknesses in a fracture-induced reservoir with TTI symmetry. Combining the linear-slip model with the Bond transformation, we have derived the stiffness matrix of a dipping-fracture-induced TTI medium characterized by normal and tangential fracture weaknesses and a tilt angle. Integrating the first-order perturbations in the stiffness matrix of a TTI medium and scattering theory, we adopt a method of azimuthal AVO parameterization for PP-wave reflection coefficient for the case of a weak-contrast interface separating two homogeneous weakly anisotropic TTI layers. We then adopt an iterative inversion method by using the partially incidence-angle-stacked seismic data with different azimuths to estimate the fracture weaknesses of a TTI medium when the tilt angle is estimated based on the image well logs prior to the seismic inversion. Synthetic examples confirm that the fracture weaknesses of a TTI medium are stably estimated from the azimuthal seismic reflected amplitudes for the case of moderate noise. A field data example demonstrates that geologically reasonable results of fracture weaknesses can be determined when the tilt angle is treated as the prior information. We determine that the azimuthal AVO inversion approach provides an available tool for fracture prediction in a dipping-fracture-induced TTI reservoir.

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An Accurate Jacobian Matrix with Exact Zoeppritz for Elastic Moduli of Dry Rock

Applied Sciences ◽

10.3390/app9245485 ◽

2019 ◽

Vol 9 (24) ◽

pp. 5485

Author(s):

Xiaobo Liu ◽

Jingyi Chen ◽

Fuping Liu ◽

Zhencong Zhao

Keyword(s):

Jacobian Matrix ◽

Incidence Angle ◽

Inversion Method ◽

Seismic Velocities ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Shear Moduli ◽

Partial Derivatives ◽

Solid Matrices ◽

Derivatives Of

Seismic velocities are related to the solid matrices and the pore fluids. The bulk and shear moduli of dry rock are the primary parameters to characterize solid matrices. Amplitude variation with offset (AVO) or amplitude variation with incidence angle (AVA) is the most used inversion method to discriminate lithology in hydrocarbon reservoirs. The bulk and shear moduli of dry rock, however, cannot be inverted directly using seismic data and the conventional AVO/AVA inversions. The most important step to accurately invert these dry rock parameters is to derive the Jacobian matrix. The combination of exact Zoeppritz and Biot–Gassmann equations makes it possible to directly calculate the partial derivatives of seismic reflectivities (PP-and PS-waves) with respect to dry rock moduli. During this research, we successfully derive the accurate partial derivatives of the exact Zoeppritz equations with respect to bulk and shear moduli of dry rock. The characteristics of these partial derivatives are investigated in the numerical examples. Additionally, we compare the partial derivatives using this proposed algorithm with the classical Shuey and Aki–Richards approximations. The results show that this derived Jacobian matrix is more accurate and versatile. It can be used further in the conventional AVO/AVA inversions to invert bulk and shear moduli of dry rock directly.

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Two-step joint PP- and PS-wave three-term amplitude-variation with offset inversion

Interpretation ◽

10.1190/int-2016-0056.1 ◽

2016 ◽

Vol 4 (4) ◽

pp. T613-T625 ◽

Cited By ~ 1

Author(s):

Qizhen Du ◽

Bo Zhang ◽

Xianjun Meng ◽

Chengfeng Guo ◽

Gang Chen ◽

...

Keyword(s):

Reflection Coefficient ◽

Wave Reflection ◽

Coefficient Matrix ◽

P Wave ◽

Inversion Method ◽

S Wave ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Avo Inversion ◽

Pp Wave

Three-term amplitude-variation with offset (AVO) inversion generally suffers from instability when there is limited prior geologic or petrophysical constraints. Two-term AVO inversion shows higher instability compared with three-term AVO inversion. However, density, which is important in the fluid-type estimation, cannot be recovered from two-term AVO inversion. To reliably predict the P- and S-waves and density, we have developed a robust two-step joint PP- and PS-wave three-term AVO-inversion method. Our inversion workflow consists of two steps. The first step is to estimate the P- and S-wave reﬂectivities using Stewart’s joint two-term PP- and PS-AVO inversion. The second step is to treat the P-wave reflectivity obtained from the first step as the prior constraint to remove the P-wave velocity related-term from the three-term Aki-Richards PP-wave approximated reflection coefficient equation, and then the reduced PP-wave reflection coefficient equation is combined with the PS-wave reflection coefficient equation to estimate the S-wave and density reﬂectivities. We determined the effectiveness of our method by first applying it to synthetic models and then to field data. We also analyzed the condition number of the coefficient matrix to illustrate the stability of the proposed method. The estimated results using proposed method are superior to those obtained from three-term AVO inversion.

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Nonlinear amplitude-variation-with-offset inversion for Lamé parameters using a direct inversion method

Interpretation ◽

10.1190/int-2016-0168.1 ◽

2017 ◽

Vol 5 (3) ◽

pp. SL57-SL67 ◽

Cited By ~ 3

Author(s):

Guangsen Cheng ◽

Xingyao Yin ◽

Zhaoyun Zong

Keyword(s):

Nonlinear Equation ◽

Real Data ◽

Seismic Inversion ◽

Inversion Method ◽

Nonlinear Inversion ◽

Reservoir Prediction ◽

Amplitude Variation ◽

Linear Inversion ◽

Amplitude Variation With Offset ◽

Avo Inversion

Prestack seismic inversion is widely used in fluid indication and reservoir prediction. Compared with linear inversion, nonlinear inversion is more precise and can be applied to high-contrast situations. The inversion results can be affected by the parameters’ sensitivity, so the parameterization of nonlinear equations is very significant. Considering the poor nonlinear amplitude-variation-with-offset (AVO) inversion results of impedance and velocity parameters, we adjust the parameters of the nonlinear equation, avoid the inaccuracy caused by parameters sensitivity and get the ideal nonlinear AVO inversion results of the Lamé parameters. The feasibility and stability of the nonlinear equation based on the Lamé parameters and method are verified by the model and the real data examples. The resolution and the lateral continuity of nonlinear inversion results are better compared with the linear inversion results.

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Enabling isotropic reflectivity modeling and inversion in anisotropic media

The Leading Edge ◽

10.1190/tle40040267.1 ◽

2021 ◽

Vol 40 (4) ◽

pp. 267-276

Author(s):

Peter Mesdag ◽

Leonardo Quevedo ◽

Cătălin Tănase

Keyword(s):

Synthetic Data ◽

Anisotropic Media ◽

Forward Modeling ◽

Seismic Inversion ◽

Stratified Medium ◽

Effective Parameters ◽

Elastic Parameters ◽

Pp Wave ◽

Anisotropic Elastic ◽

And Inversion

Exploration and development of unconventional reservoirs, where fractures and in-situ stresses play a key role, call for improved characterization workflows. Here, we expand on a previously proposed method that makes use of standard isotropic modeling and inversion techniques in anisotropic media. Based on approximations for PP-wave reflection coefficients in orthorhombic media, we build a set of transforms that map the isotropic elastic parameters used in prestack inversion into effective anisotropic elastic parameters. When used in isotropic forward modeling and inversion, these effective parameters accurately mimic the anisotropic reflectivity behavior of the seismic data, thus closing the loop between well-log data and seismic inversion results in the anisotropic case. We show that modeling and inversion of orthorhombic anisotropic media can be achieved by superimposing effective elastic parameters describing the behavior of a horizontally stratified medium and a set of parallel vertical fractures. The process of sequential forward modeling and postinversion analysis is exemplified using synthetic data.

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Multiazimuthal modeling and inversion of qP reflection coefficients in fractured media

Geophysics ◽

10.1190/1.1444621 ◽

1999 ◽

Vol 64 (4) ◽

pp. 1143-1152 ◽

Cited By ~ 1

Author(s):

Ivan A. Simões‐Filho ◽

Fernando A. Neves ◽

Júlio S. Tinen ◽

João S. Protázio ◽

Jessé C. Costa

Keyword(s):

Isotropic Medium ◽

Model Space ◽

Transversely Isotropic ◽

Reservoir Rock ◽

Reflection Coefficients ◽

Fracture Density ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

The Difference ◽

And Inversion

We present a method for the exact modeling and inversion of multiazimuthal qP-wave reflection coefficients at an interface separating two anisotropic media. This procedure can be used for media with at least one of its planes of symmetry parallel to the interface (i.e., monoclinic or higher symmetries). To illustrate the method, we compute qP-wave reflection coefficients at an interface separating an isotropic medium (representing a seal rock) from a transversely isotropic medium (representing a reservoir rock with vertical aligned fractures). Forward modeling shows that the difference in the offset of the critical angles for different azimuths is proportional to the fracture density: the higher the fracture density, the larger the difference. In the second part of the paper, we use a global optimization technique (genetic algorithm) to invert wide‐angle amplitude variation with offset (AVO) synthetic data. The model space consists of mass density and five elastic parameters of a transversely isotropic medium with a horizontal symmetry axis (HTI medium), which, to the first order, represents the fractured reservoir rock. For this model, we find that the configuration of three azimuths of data acquisition is the minimum number of acquisition planes needed to invert amplitude variation with offset/amplitude variation with azimuth (AVO/AVA) data. Further, there is a need for incidence angles up to 40°; a more narrow range of angles can lead to models that fit the data perfectly only up to the “maximum” incidence angle. We assume that the velocities and density of the isotropic rock are known, but use no prior information on the values of the model space parameters of the fractured rock except for reasonable velocity values in crustal rocks and constraints of elastic stability of solid media. After inversion for the model space parameters, we compute statistics of the 30 best models and likelihood functions, which provide information on the nonuniqueness and quality of the AVO/AVA inverse problem.

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Amplitude-variation-with-offset, elastic-impedence, and wave-equation synthetics — A modeling study

Geophysics ◽

10.1190/1.2387108 ◽

2007 ◽

Vol 72 (1) ◽

pp. C1-C7 ◽

Cited By ~ 29

Author(s):

Subhashis Mallick

Keyword(s):

Wave Equation ◽

Incidence Angle ◽

Synthetic Data ◽

P Wave ◽

Equation Modeling ◽

Parameter Estimates ◽

Angle Of Incidence ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Wave Modes

Amplitude-variation-with-offset (AVO) and elastic-impedance (EI) analysis use an approximate plane P-wave reflection coefficient as a function of angle of incidence. AVO and EI both can be used in a three-term or a two-term formulation. This study uses synthetic data to demonstrate that the P-wave primary reflections at large offsets can be contaminated by reflections from other wave modes that can affect the quality of three-term AVO or EI results. The coupling of P-waves and S-waves in seismic-wave propagation through finely layered media generates the interfering wave modes. A methodology such as prestack-wave-equation modeling can properly account for these coupling effects. Both AVO and EI also assume a convolutional model whose accuracy decreases as incidence angles increase. On the other hand, wave-equation modeling is based on the rigorous solution to the wave equation and is valid for any incidence angle. Because wave interference is minimal at small angles, a two-term AVO/EI analysis that restricts input from small angles is likely to give more reliable parameter estimates than a three-term analysis. A three-term AVO/EI analysis should be used with caution and should be calibrated against well data and other data before being used for quantitative analysis.

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Prestack waveform inversion of three-dimensional seismic data — An example from the Rock Springs Uplift, Wyoming, USA

Geophysics ◽

10.1190/geo2016-0079.1 ◽

2017 ◽

Vol 82 (1) ◽

pp. B1-B12 ◽

Cited By ~ 5

Author(s):

Josiane Pafeng ◽

Subhashis Mallick ◽

Hema Sharma

Keyword(s):

Seismic Data ◽

Reservoir Characterization ◽

Waveform Inversion ◽

Three Dimensional ◽

Seismic Inversion ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Seismic Waveform ◽

Rock Springs Uplift ◽

Rock Springs

Applying seismic inversion to estimate subsurface elastic earth properties for reservoir characterization is a challenge in exploration seismology. In recent years, waveform-based seismic inversions have gained popularity, but due to high computational costs, their applications are limited, and amplitude-variation-with-offset/angle inversion is still the current state-of-the-art. We have developed a genetic-algorithm-based prestack seismic waveform inversion methodology. By parallelizing at multiple levels and assuming a locally 1D structure such that forward computation of wave equation synthetics is computationally efficient, this method is capable of inverting 3D prestack seismic data on parallel computers. Applying this inversion to a real prestack seismic data volume from the Rock Springs Uplift (RSU) located in Wyoming, USA, we determined that our method is capable of inverting the data in a reasonable runtime and producing much higher quality results than amplitude-variation-with-offset/angle inversion. Because the primary purpose for seismic data acquisition at the RSU was to characterize the subsurface for potential targets for carbon dioxide sequestration, we also identified and analyzed some potential primary and secondary storage formations and their associated sealing lithologies from our inversion results.

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Computation of dry-rock VP/VS ratio, fluid property factor, and density estimation from amplitude-variation-with-offset inversion

Geophysics ◽

10.1190/geo2017-0621.1 ◽

2018 ◽

Vol 83 (6) ◽

pp. R669-R679 ◽

Cited By ~ 1

Author(s):

Gang Chen ◽

Xiaojun Wang ◽

Baocheng Wu ◽

Hongyan Qi ◽

Muming Xia

Keyword(s):

Reservoir Characterization ◽

Synthetic Data ◽

Pore Fluid ◽

Inversion Method ◽

S Wave ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Fluid Identification ◽

Fluid Property ◽

Avo Inversion

Estimating the fluid property factor and density from amplitude-variation-with-offset (AVO) inversion is important for fluid identification and reservoir characterization. The fluid property factor can distinguish pore fluid in the reservoir and the density estimate aids in evaluating reservoir characteristics. However, if the scaling factor of the fluid property factor (the dry-rock [Formula: see text] ratio) is chosen inappropriately, the fluid property factor is not only related to the pore fluid, but it also contains a contribution from the rock skeleton. On the other hand, even if the angle gathers include large angles (offsets), a three-parameter AVO inversion struggles to estimate an accurate density term without additional constraints. Thus, we have developed an equation to compute the dry-rock [Formula: see text] ratio using only the P- and S-wave velocities and density of the saturated rock from well-logging data. This decouples the fluid property factor from lithology. We also developed a new inversion method to estimate the fluid property factor and density parameters, which takes full advantage of the high stability of a two-parameter AVO inversion. By testing on a portion of the Marmousi 2 model, we find that the fluid property factor calculated by the dry-rock [Formula: see text] ratio obtained by our method relates to the pore-fluid property. Simultaneously, we test the AVO inversion method for estimating the fluid property factor and density parameters on synthetic data and analyze the feasibility and stability of the inversion. A field-data example indicates that the fluid property factor obtained by our method distinguishes the oil-charged sand channels and the water-wet sand channel from the well logs.

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Joint anisotropic amplitude variation with offset inversion of PP and PS seismic data

Geophysics ◽

10.1190/geo2016-0516.1 ◽

2018 ◽

Vol 83 (2) ◽

pp. N31-N50 ◽

Cited By ~ 8

Author(s):

Jun Lu ◽

Yun Wang ◽

Jingyi Chen ◽

Ying An

Keyword(s):

Seismic Data ◽

Local Minimum ◽

Synthetic Data ◽

Inversion Method ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Avo Inversion ◽

Time Migration ◽

Amplitude Variation With Angle ◽

Two Stages

With the increase in exploration target complexity, more parameters are required to describe subsurface properties, particularly for finely stratified reservoirs with vertical transverse isotropic (VTI) features. We have developed an anisotropic amplitude variation with offset (AVO) inversion method using joint PP and PS seismic data for VTI media. Dealing with local minimum solutions is critical when using anisotropic AVO inversion because more parameters are expected to be derived. To enhance the inversion results, we adopt a hierarchical inversion strategy to solve the local minimum solution problem in the Gauss-Newton method. We perform the isotropic and anisotropic AVO inversions in two stages; however, we only use the inversion results from the first stage to form search windows for constraining the inversion in the second stage. To improve the efficiency of our method, we built stop conditions using Euclidean distance similarities to control iteration of the anisotropic AVO inversion in noisy situations. In addition, we evaluate a time-aligned amplitude variation with angle gather generation approach for our anisotropic AVO inversion using anisotropic prestack time migration. We test the proposed method on synthetic data in ideal and noisy situations, and find that the anisotropic AVO inversion method yields reasonable inversion results. Moreover, we apply our method to field data to show that it can be used to successfully identify complex lithologic and fluid information regarding fine layers in reservoirs.

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Inversion and interpretation of seismic-derived rock properties in the Duvernay play

Interpretation ◽

10.1190/int-2017-0149.1 ◽

2018 ◽

Vol 6 (2) ◽

pp. SE1-SE14 ◽

Cited By ~ 13

Author(s):

Ronald M. Weir ◽

David W. Eaton ◽

Larry R. Lines ◽

Donald C. Lawton ◽

Eneanwan Ekpo

Keyword(s):

Joint Inversion ◽

Seismic Inversion ◽

Rock Properties ◽

Data Set ◽

Structural Mapping ◽

Amplitude Variation With Offset ◽

Multicomponent Seismic ◽

Depth Relationship ◽

And Inversion

We have developed an interpretive seismic workflow that incorporates multicomponent seismic inversion, guided by structural mapping, for characterizing low-permeability unconventional reservoirs. The workflow includes the determination of a calibrated time-depth relationship, generation of seismic-derived structural maps, poststack inversion, amplitude-variation-with-offset analysis, and PP-PS joint inversion. The subsequent interpretation procedure combines structural and inversion results with seismic-derived lithologic parameters, such as the Young’s modulus, Poisson’s ratio, and brittleness index. We applied this workflow to a 3D multicomponent seismic data set from the Duvernay play in the Kaybob area in Alberta, Canada. Subtle faults are discernible using isochron maps, horizontal time slices, and seismic stratal slices. Fault-detection software is also used to aid in the delineation of structural discontinuities. We found that seismic-derived attributes, coupled with structural mapping, can be used to map reservoir facies and thus to highlight zones that are most favorable for hydraulic-fracture stimulation. By imaging structural discontinuities and preexisting zones of weakness, seismic mapping also contributes to an improved framework for understanding the induced-seismicity risk.

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